%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO052^2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:49 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO052^2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n026.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:27:43 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.26 % (811511)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (811520)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2850302790:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.26 % (811517)% WARNING: option uhcvi not known.
% 0.08/0.26 % (811520)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (811516)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1765156371_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.26 % (811518)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3558561547:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (811517)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3098966451:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (811519)dis+10_1_sil=32000:sp=arity:random_seed=2043895617:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.26 % (811521)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3538186579:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.26 % (811517)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % Exception at run slice level
% 0.08/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.26 % (811517)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.26 % (811520) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-811511-811520"...
% 0.08/0.26 % (811522)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1923544197:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.26 % (811520)...printing done.
% 0.08/0.26 % (811520)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, mu: $tType).
% 0.08/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(func_def_0, type, meq_ind: (mu > mu > $i > $o)).
% 0.08/0.26 thf(func_def_1, type, meq_prop: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_4, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_5, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_6, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_7, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_8, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_9, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_10, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_11, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_12, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_13, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_14, type, mtrue: ($i > $o)).
% 0.08/0.26 thf(func_def_15, type, mfalse: ($i > $o)).
% 0.08/0.26 thf(func_def_16, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_17, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_18, type, mreflexive: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_19, type, msymmetric: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_20, type, mserial: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_21, type, mtransitive: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_22, type, meuclidean: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_23, type, mpartially_functional: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_24, type, mfunctional: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_25, type, mweakly_dense: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_26, type, mweakly_connected: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_27, type, mweakly_directed: (($i > $i > $o) > $o)).
% 0.08/0.26 thf(func_def_28, type, mvalid: (($i > $o) > $o)).
% 0.08/0.26 thf(func_def_29, type, minvalid: (($i > $o) > $o)).
% 0.08/0.26 thf(func_def_30, type, msatisfiable: (($i > $o) > $o)).
% 0.08/0.26 thf(func_def_31, type, mcountersatisfiable: (($i > $o) > $o)).
% 0.08/0.26 thf(func_def_32, type, r: ($i > $i > $o)).
% 0.08/0.26 thf(func_def_33, type, a: ($i > $o)).
% 0.08/0.26 thf(func_def_34, type, b: ($i > $o)).
% 0.08/0.26 thf(func_def_35, type, db2: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_36, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_37, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.08/0.26 thf(func_def_38, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.26 thf(func_def_39, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_40, type, vNOT: ($o > $o)).
% 0.08/0.26 thf(func_def_41, type, vOR: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_42, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.26 thf(func_def_45, type, db3: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_46, type, vIMP: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_47, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.26 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_49, type, db4: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_50, type, sK0: (($i > $o) > $i > ($i > $i > $o) > $i)).
% 0.08/0.26 thf(func_def_51, type, sK1: (($i > $o) > $i > ($i > $i > $o) > ($i > $o) > $i)).
% 0.08/0.26 thf(func_def_52, type, sK2: ($i > ($i > $i > $o) > ($i > $o) > $i)).
% 0.08/0.26 thf(f3,axiom,(
% 0.08/0.26 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot)).
% 0.08/0.26 thf(f4,axiom,(
% 0.08/0.26 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor)).
% 0.08/0.26 thf(f6,axiom,(
% 0.08/0.26 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies)).
% 0.08/0.26 thf(f11,axiom,(
% 0.08/0.26 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop)).
% 0.08/0.26 thf(f16,axiom,(
% 0.08/0.26 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox)).
% 0.08/0.26 thf(f17,axiom,(
% 0.08/0.26 (mdia = (^[X0 : ($i > $i > $o), X1 : ($i > $o)] : ((mnot @ (mbox @ X0 @ (mnot @ X1))))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia)).
% 0.08/0.26 thf(f28,axiom,(
% 0.08/0.26 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid)).
% 0.08/0.26 thf(f32,conjecture,(
% 0.08/0.26 ? [X0 : ($i > $i > $o)] : ~(mvalid @ (mforall_prop @ (^[X1 : ($i > $o)] : ((mforall_prop @ (^[X2 : ($i > $o)] : ((mimplies @ (mbox @ X0 @ (mimplies @ X1 @ X2)) @ (mimplies @ (mbox @ X0 @ X1) @ (mdia @ X0 @ X2))))))))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.08/0.26 thf(f33,negated_conjecture,(
% 0.08/0.26 ~ ? [X0 : ($i > $i > $o)] : ~(mvalid @ (mforall_prop @ (^[X1 : ($i > $o)] : ((mforall_prop @ (^[X2 : ($i > $o)] : ((mimplies @ (mbox @ X0 @ (mimplies @ X1 @ X2)) @ (mimplies @ (mbox @ X0 @ X1) @ (mdia @ X0 @ X2))))))))))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f32])).
% 0.08/0.26 thf(f36,plain,(
% 0.08/0.26 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.08/0.26 inference(rectify,[],[f3])).
% 0.08/0.26 thf(f37,plain,(
% 0.08/0.26 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.08/0.26 inference(fool_elimination,[],[f36])).
% 0.08/0.26 thf(f38,plain,(
% 0.08/0.26 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.08/0.26 inference(rectify,[],[f4])).
% 0.08/0.26 thf(f39,plain,(
% 0.08/0.26 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.08/0.26 inference(fool_elimination,[],[f38])).
% 0.08/0.26 thf(f41,plain,(
% 0.08/0.26 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.08/0.26 inference(fool_elimination,[],[f6])).
% 0.08/0.26 thf(f47,plain,(
% 0.08/0.26 (mforall_prop = (^[X0 : (($i > $o) > $i > $o), X1 : $i] : (! [X2 : ($i > $o)] : (X0 @ X2 @ X1))))),
% 0.08/0.26 inference(rectify,[],[f11])).
% 0.08/0.26 thf(f48,plain,(
% 0.08/0.26 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.08/0.26 inference(fool_elimination,[],[f47])).
% 0.08/0.26 thf(f54,plain,(
% 0.08/0.26 (mbox = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 0.08/0.26 inference(rectify,[],[f16])).
% 0.08/0.26 thf(f55,plain,(
% 0.08/0.26 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.08/0.26 inference(fool_elimination,[],[f54])).
% 0.08/0.26 thf(f56,plain,(
% 0.08/0.26 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.08/0.26 inference(fool_elimination,[],[f17])).
% 0.08/0.26 thf(f77,plain,(
% 0.08/0.26 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.08/0.26 inference(rectify,[],[f28])).
% 0.08/0.26 thf(f78,plain,(
% 0.08/0.26 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.08/0.26 inference(fool_elimination,[],[f77])).
% 0.08/0.26 thf(f85,plain,(
% 0.08/0.26 ~ ? [X0 : ($i > $i > $o)] : ~(mvalid @ (mforall_prop @ (^[X1 : ($i > $o)] : ((mforall_prop @ (^[X2 : ($i > $o)] : ((mimplies @ (mbox @ X0 @ (mimplies @ X1 @ X2)) @ (mimplies @ (mbox @ X0 @ X1) @ (mdia @ X0 @ X2))))))))))),
% 0.08/0.26 inference(rectify,[],[f33])).
% 0.08/0.26 thf(f86,plain,(
% 0.08/0.26 ~ ? [X0 : ($i > $i > $o)] : ~ ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mbox @ X0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y1))))))))))),
% 0.08/0.26 inference(fool_elimination,[],[f85])).
% 0.08/0.26 thf(f87,plain,(
% 0.08/0.26 ~ ? [X0 : ($i > $i > $o)] : ($true != ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mbox @ X0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y1))))))))))),
% 0.08/0.26 inference(flattening,[],[f86])).
% 0.08/0.26 thf(f88,plain,(
% 0.08/0.26 ! [X0 : ($i > $i > $o)] : ($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mbox @ X0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y1))))))))))),
% 0.08/0.26 inference(ennf_transformation,[],[f87])).
% 0.08/0.26 thf(f91,plain,(
% 0.08/0.26 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f37])).
% 0.08/0.26 thf(f92,plain,(
% 0.08/0.26 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f39])).
% 0.08/0.26 thf(f94,plain,(
% 0.08/0.26 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.08/0.26 inference(cnf_transformation,[],[f41])).
% 0.08/0.26 thf(f99,plain,(
% 0.08/0.26 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f48])).
% 0.08/0.26 thf(f104,plain,(
% 0.08/0.26 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f55])).
% 0.08/0.26 thf(f105,plain,(
% 0.08/0.26 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f56])).
% 0.08/0.26 thf(f116,plain,(
% 0.08/0.26 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.08/0.26 inference(cnf_transformation,[],[f78])).
% 0.08/0.26 thf(f120,plain,(
% 0.08/0.26 ( ! [X0 : ($i > $i > $o)] : (($true = ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mimplies @ (mbox @ X0 @ (mimplies @ Y0 @ Y1)) @ (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y1))))))))))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f88])).
% 0.08/0.26 thf(f121,definition,(
% 0.08/0.26 ($true != $false)),
% 0.08/0.26 introduced(theory,[fool_distinctness_axiom])).
% 0.08/0.26 thf(f124,plain,(
% 0.08/0.26 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.08/0.26 inference(definition_unfolding,[],[f94,f92,f91])).
% 0.08/0.26 thf(f131,plain,(
% 0.08/0.26 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.08/0.26 inference(definition_unfolding,[],[f105,f91,f104,f91])).
% 0.08/0.26 thf(f132,plain,(
% 0.08/0.26 ( ! [X0 : ($i > $i > $o)] : (($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : ($i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ X0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1)) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ X0 @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y4 @ Y6 @ Y7)) | (Y5 @ Y7))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ X0 @ Y1))))))))))) )),
% 0.08/0.26 inference(definition_unfolding,[],[f120,f116,f99,f99,f124,f104,f124,f124,f104,f131])).
% 0.08/0.26 thf(f133,plain,(
% 0.08/0.26 ( ! [X0 : ($i > $i > $o)] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (X0 @ Y0 @ Y3)) | ((~ (Y1 @ Y3)) | (Y2 @ Y3)))))) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (X0 @ Y0 @ Y3)) | (Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (X0 @ Y0 @ Y3)) | (~ (Y2 @ Y3))))))))))))))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f132])).
% 0.08/0.26 thf(f134,plain,(
% 0.08/0.26 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (X0 @ Y0 @ Y3)) | ((~ (Y1 @ Y3)) | (Y2 @ Y3)))))) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (X0 @ Y0 @ Y3)) | (Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (X0 @ Y0 @ Y3)) | (~ (Y2 @ Y3))))))))))))) @ X1)))) )),
% 0.08/0.26 inference(pi_proxy_clausification,[],[f133])).
% 0.08/0.26 thf(f135,plain,(
% 0.08/0.26 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (X0 @ X1 @ Y2)) | ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (X0 @ X1 @ Y2)) | (Y0 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (X0 @ X1 @ Y2)) | (~ (Y1 @ Y2))))))))))))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f134])).
% 0.08/0.26 thf(f136,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (X0 @ X1 @ Y2)) | ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (X0 @ X1 @ Y2)) | (Y0 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (X0 @ X1 @ Y2)) | (~ (Y1 @ Y2))))))))))) @ X2)))) )),
% 0.08/0.26 inference(pi_proxy_clausification,[],[f135])).
% 0.08/0.26 thf(f137,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X0 @ X1 @ Y1)) | ((~ (X2 @ Y1)) | (Y0 @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X0 @ X1 @ Y1)) | (X2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (X0 @ X1 @ Y1)) | (~ (Y0 @ Y1))))))))))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f136])).
% 0.08/0.26 thf(f138,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X0 @ X1 @ Y1)) | ((~ (X2 @ Y1)) | (Y0 @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (X0 @ X1 @ Y1)) | (X2 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (X0 @ X1 @ Y1)) | (~ (Y0 @ Y1))))))))) @ X3)))) )),
% 0.08/0.26 inference(pi_proxy_clausification,[],[f137])).
% 0.08/0.26 thf(f139,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | ((~ (X2 @ Y0)) | (X3 @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (X2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (~ (X3 @ Y0))))))))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f138])).
% 0.08/0.26 thf(f140,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (X2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (~ (X3 @ Y0))))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | ((~ (X2 @ Y0)) | (X3 @ Y0))))))))) )),
% 0.08/0.26 inference(or_proxy_clausification,[],[f139])).
% 0.08/0.26 thf(f141,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (~ (X3 @ Y0)))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | ((~ (X2 @ Y0)) | (X3 @ Y0)))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 0.08/0.26 inference(or_proxy_clausification,[],[f140])).
% 0.08/0.26 thf(f142,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (~ (X3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | ((~ (X2 @ Y0)) | (X3 @ Y0)))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 0.08/0.26 inference(not_proxy_clausification,[],[f141])).
% 0.08/0.26 thf(f143,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (~ (X3 @ Y0)))) @ (sK0 @ X3 @ X1 @ X0)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | ((~ (X2 @ Y0)) | (X3 @ Y0)))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 0.08/0.26 inference(sigma_proxy_clausification,[],[f142])).
% 0.08/0.26 thf(f144,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (~ (X3 @ Y0)))) @ (sK0 @ X3 @ X1 @ X0)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | ((~ (X2 @ Y0)) | (X3 @ Y0))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 0.08/0.26 inference(not_proxy_clausification,[],[f143])).
% 0.08/0.26 thf(f145,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (~ (X3 @ Y0)))) @ (sK0 @ X3 @ X1 @ X0)))) | ($false = (((^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | ((~ (X2 @ Y0)) | (X3 @ Y0)))) @ (sK1 @ X3 @ X1 @ X0 @ X2)))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (X2 @ Y0)))))))) )),
% 0.08/0.26 inference(sigma_proxy_clausification,[],[f144])).
% 0.08/0.26 thf(f146,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (~ (X3 @ Y0)))) @ (sK0 @ X3 @ X1 @ X0)))) | ($false = (((^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | ((~ (X2 @ Y0)) | (X3 @ Y0)))) @ (sK1 @ X3 @ X1 @ X0 @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (X2 @ Y0))))))) )),
% 0.08/0.26 inference(not_proxy_clausification,[],[f145])).
% 0.08/0.26 thf(f147,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (~ (X3 @ Y0)))) @ (sK0 @ X3 @ X1 @ X0)))) | ($false = (((^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | ((~ (X2 @ Y0)) | (X3 @ Y0)))) @ (sK1 @ X3 @ X1 @ X0 @ X2)))) | ($false = (((^[Y0 : $i]: ((~ (X0 @ X1 @ Y0)) | (X2 @ Y0))) @ (sK2 @ X1 @ X0 @ X2))))) )),
% 0.08/0.26 inference(sigma_proxy_clausification,[],[f146])).
% 0.08/0.26 thf(f148,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($false = (((~ (X0 @ X1 @ (sK0 @ X3 @ X1 @ X0))) | (~ (X3 @ (sK0 @ X3 @ X1 @ X0)))))) | ($false = (((~ (X0 @ X1 @ (sK1 @ X3 @ X1 @ X0 @ X2))) | ((~ (X2 @ (sK1 @ X3 @ X1 @ X0 @ X2))) | (X3 @ (sK1 @ X3 @ X1 @ X0 @ X2)))))) | ($false = (((~ (X0 @ X1 @ (sK2 @ X1 @ X0 @ X2))) | (X2 @ (sK2 @ X1 @ X0 @ X2)))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f147])).
% 0.08/0.26 thf(f149,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($false = ((~ (X3 @ (sK0 @ X3 @ X1 @ X0))))) | ($false = (((~ (X0 @ X1 @ (sK1 @ X3 @ X1 @ X0 @ X2))) | ((~ (X2 @ (sK1 @ X3 @ X1 @ X0 @ X2))) | (X3 @ (sK1 @ X3 @ X1 @ X0 @ X2)))))) | ($false = (((~ (X0 @ X1 @ (sK2 @ X1 @ X0 @ X2))) | (X2 @ (sK2 @ X1 @ X0 @ X2)))))) )),
% 0.08/0.26 inference(or_proxy_clausification,[],[f148])).
% 0.08/0.26 thf(f167,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = ((X3 @ (sK0 @ X3 @ X1 @ X0)))) | ($false = (((~ (X0 @ X1 @ (sK1 @ X3 @ X1 @ X0 @ X2))) | ((~ (X2 @ (sK1 @ X3 @ X1 @ X0 @ X2))) | (X3 @ (sK1 @ X3 @ X1 @ X0 @ X2)))))) | ($false = (((~ (X0 @ X1 @ (sK2 @ X1 @ X0 @ X2))) | (X2 @ (sK2 @ X1 @ X0 @ X2)))))) )),
% 0.08/0.26 inference(not_proxy_clausification,[],[f149])).
% 0.08/0.26 thf(f169,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = ((X3 @ (sK0 @ X3 @ X1 @ X0)))) | ($false = ((~ (X0 @ X1 @ (sK1 @ X3 @ X1 @ X0 @ X2))))) | ($false = (((~ (X0 @ X1 @ (sK2 @ X1 @ X0 @ X2))) | (X2 @ (sK2 @ X1 @ X0 @ X2)))))) )),
% 0.08/0.26 inference(or_proxy_clausification,[],[f167])).
% 0.08/0.26 thf(f170,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = ((X3 @ (sK0 @ X3 @ X1 @ X0)))) | ($true = ((X0 @ X1 @ (sK1 @ X3 @ X1 @ X0 @ X2)))) | ($false = (((~ (X0 @ X1 @ (sK2 @ X1 @ X0 @ X2))) | (X2 @ (sK2 @ X1 @ X0 @ X2)))))) )),
% 0.08/0.26 inference(not_proxy_clausification,[],[f169])).
% 0.08/0.26 thf(f171,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true = ((X3 @ (sK0 @ X3 @ X1 @ X0)))) | ($true = ((X0 @ X1 @ (sK1 @ X3 @ X1 @ X0 @ X2)))) | ($false = ((X2 @ (sK2 @ X1 @ X0 @ X2))))) )),
% 0.08/0.26 inference(or_proxy_clausification,[],[f170])).
% 0.08/0.26 thf(f241,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i] : (($true = ((X3 @ (sK0 @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false)))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X1 @ (sK1 @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X2)))) | ($false = ((X2 @ (sK2 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X2))))) )),
% 0.08/0.26 inference(primitive_instantiation,[],[f171])).
% 0.08/0.26 thf(f330,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i] : (($true = ((X3 @ (sK0 @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false)))))))) | ($true = $false) | ($false = ((X2 @ (sK2 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X2))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f241])).
% 0.08/0.26 thf(f331,plain,(
% 0.08/0.26 ( ! [X2 : ($i > $o),X3 : ($i > $o),X1 : $i] : (($true = ((X3 @ (sK0 @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false)))))))) | ($false = ((X2 @ (sK2 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X2))))) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f330])).
% 0.08/0.26 thf(f368,plain,(
% 0.08/0.26 ( ! [X0 : $i,X1 : ($i > $o)] : (($false != $false) | ($true = ((X1 @ (sK0 @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false))))))))) )),
% 0.08/0.26 inference(constrained_superposition,[],[f121,f331])).
% 0.08/0.26 thf(f399,plain,(
% 0.08/0.26 ( ! [X0 : $i,X1 : ($i > $o)] : (($true = ((X1 @ (sK0 @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false))))))))) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f368])).
% 0.08/0.26 thf(f600,plain,(
% 0.08/0.26 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: ($false)) @ (sK0 @ (^[Y0 : $i]: ($false)) @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false))))))))) )),
% 0.08/0.26 inference(primitive_instantiation,[],[f399])).
% 0.08/0.26 thf(f635,plain,(
% 0.08/0.26 ($true = $false)),
% 0.08/0.26 inference(beta-eta_normalization,[],[f600])).
% 0.08/0.26 thf(f636,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f635])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (811520)------------------------------
% 0.08/0.26 % (811520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (811520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (811520)CaDiCaL version: 2.1.3
% 0.08/0.26 % (811520)Termination reason: Refutation
% 0.08/0.26 % (811520)Time elapsed: 0.021 s
% 0.08/0.26 % (811520)Peak memory usage: 12 MB
% 0.08/0.26 % (811520)Instructions burned: 55 (million)
% 0.08/0.26 % (811511)Success in time 0.051 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------